Geometry

Question 1

vertex, vertices

Answer 1

sommet

Question 2

acute angle

Answer 2

< 90°

Question 3

obtuse angle

Answer 3

> 90°

Question 4

area of a triangle

Answer 4

A = (1/2)bh
b : base
h : height (altitude)

Question 5

altitude of a triangle

Answer 5

line that goes through the vertex and is perpendicular to the opposite side

Question 6

legs

Answer 6

sides of a triangle that meet at the right angle
in a right triangle, the legs represent two of its altitudes. If one leg is the base, the other leg is the altitude, and the area equals 1/2 times the product of the legs

Question 7

median of a triangle

Answer 7

goes from a vertex to the midpoint of the opposite side

Question 8

Pythagorean theorem

Answer 8

hypotenuse² = leg² + leg²

Question 9

Pythagorean triplets

Answer 9

sets of integers that satisfy the theorem
3, 4, 5
5, 12, 13
8, 15, 17
7, 24, 25

we could also multiply any of these fundamental triplets by any nb to create a new set of three nb
6, 8, 10
9, 12, 15
12, 16, 20
15, 20, 25
18, 20, 25
...

Question 10

scale factor

Answer 10

Similar triangles
scale factor = ratio: lengths of sides are proportional so k is the factor by which all lengths in the small figure were multiplied to arrive at the lengths in the large figure
when lenghts are multiplied by scale factor k, area is multiplied by k²

Question 11

similar figures

Answer 11

same shape but different size
angles are equal 
two triangles are similar if they simply share two angles
sides are proportional
scale factor

Question 12

Isosceles right triangle

Answer 12

angles of 45°-45°-90°
sides of 1-1-√2
two equal legs, and (hypotenuse) = (√2)*(leg)

Question 13

equilateral triangle + altitude = right triangles

Answer 13

angles of 30°-60°-90°
sides of 1-√3-2
hypotenuse = 2 * short leg
long leg = √3 * short leg

Question 14

rhombuses

Answer 14

parallelograms with four sides equal and perpendicular diagonals

Question 15

area of a trapezoid

Answer 15

find the average of the bases, and multiply this by the height
A = ((b1 + b2)/2)h

or subdivide the trapezoid into a central rectangle and two side right triangles (in a symmetrical trapezoid, those two side right triangles will be congruent)

Question 16

area of a quadrilateral

Answer 16

A = bh

Question 17

pentagon

Answer 17

a polygon with 5 vertices, sides, and diagonals
can be broken into three triangles
sum of the angles = 540°

Question 18

hexagon

Answer 18

a polygon with 6 vertices and sides
9diagonals
can be broken into four triangles
sum of the angles = 720°

Question 19

regular polygon

Answer 19

equilateral and equiangular: most symmetrical and well-balanced example of a category
regular triangle = equilateral
regular quadrilateral = square
regular pentagon: each angle = 108°
regular hexagon: each angle = 120°
regular octagon: each angle = 135°; sum of angles = 1080°

Question 20

chord

Answer 20

a segment with 2 endpoints on the circle

the longest chord passes through the center and is called a diameter

Question 21

circumference of a circle

Answer 21

c = πd
c = 2πr

Question 22

π approximations

Answer 22

3.14

22/7

Question 23

area of a circle

Answer 23

A = πr²

Question 24

inscribed angle and central angle relationship with the arc they intercept (circle properties)

Answer 24

the measure of a central angle is the measure of the arc it intercepts
the measure of an inscribed angle is HALF the measure of the arc it intercepts

Question 25

Circle propertiesr

Answer 25

if two sides of a triangle are radii, the triangle is isosceles

a central angle has the same measure as the arc it intercepts

equal length chords intercept equal arcs

an inscribed angle has half the measure of the arc it intercepts

an angle inscribed in a semicircle is 90°

two inscribed angles intersecting the same chord on the same side are equal

a tangent line is perpendicular to a radius at the point of tangency

Question 26

proportion of an arclength

Answer 26

arclength/2πr(circumference) = angle/360

Question 27

ratio of areas to the ratio of angles

Answer 27

area of sector/πr² = angle/360

Question 28

total volume and surface area of a cube

total volume and surface area of a rectangle

Answer 28

V = s^3; SA = 6s²
V = hwd; SA = 2hw + 2hd + 2wd

Question 29

3D version of the Pythagorean theorem

Answer 29

AD² = AB² + BC² + CD²

Question 30

diagonal of a square

space diagonal of a cube

Answer 30

side*√2

side*√3

Question 31

volume of a cylinder

Answer 31

V = πr²h

Question 32

total surface area of a cylinder

Answer 32

2πr²+2πrh

2x surface of circle + surface of rectangle

Question 33

A cylinder neatly encloses a sphere, so that the curve of the cylinder touches the sphere in a circle at its widest, and the top & bottom faces of the cylinder are tangent to the sphere. If the volume of the sphere is V = 4/3 * πr^3, what fraction of the cylinder does the sphere occupy?

Answer 33

the radius of the sphere and that of the cylinder must be the same, r

the height of the cylinder must be as tall as the sphere, so it must equal the diameter, h = 2r

cylinder; V = πr²h = πr²2r = 2πr^3

if we divide 4/3 * πr^3 by 2πr^3, the πr^3 parts will cancel, and we will just be left with (4/3)/2 = 2/3

Question 34

Between two similar figures, if the length increases by scale factor k, the area increases by… and the volume increases by…

Answer 34

ratio of the lengths: k
ratio of the surfaces: k²
ratio of the volumes: k^3

Question 35

A bathroom floor is a rectangle, 2m by 3m. it is to be tiled with square tiles, 4cm on a side. How many tiles will it take to fill the floor? (1m = 100cm)

Answer 35

area = 6m²(100cm/1m)² = 60 000cm^3
divide this by 4cm² (= divide by 4 twice)
60000/4 = 15000
15000/4 = (16000 - 1000) /4 = 3750

Question 36

A swimming pool has the capacity of a rectangular solid 5m x 8m on the surface and 2m deep. The pool is filled with grains of sand. If each grain of sand is 1mm^3, and 1m = 1000mm, how many grains of sand are in the pool?

Answer 36

V = 2*5*8 = 80m^3
(80m^3)(1000mm/1m)^3 = 80(10^3)^3 = 80(10^9) = 8(10^10)